What is the integral from 1 to 2 of (10-5x)/(x^3) ?

The integral from 1 to 2 of (10-5x)/(x^3) is 5/4

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integral from 1 to 2 of (10-5x)/(x^3)

\int_{1}^{2} \frac{10 - 5 x}{x ^{3}} d x

\frac{5}{4}

Solution steps

\int_{1}^{2} \frac{10 - 5 x}{x ^{3}} d x

Expand

\frac{10 - 5 x}{x ^{3}} : \frac{10}{x ^{3}} - \frac{5}{x ^{2}}

= \int_{1}^{2} \frac{10}{x ^{3}} - \frac{5}{x ^{2}} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{1}^{2} \frac{10}{x ^{3}} d x - \int_{1}^{2} \frac{5}{x ^{2}} d x

\int_{1}^{2} \frac{10}{x ^{3}} d x = \frac{15}{4}

\int_{1}^{2} \frac{5}{x ^{2}} d x = \frac{5}{2}

= \frac{15}{4} - \frac{5}{2}

Simplify

\frac{15}{4} - \frac{5}{2} : \frac{5}{4}

= \frac{5}{4}

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What is the integral from 1 to 2 of (10-5x)/(x^3) ?
The integral from 1 to 2 of (10-5x)/(x^3) is 5/4